A047377 Numbers that are congruent to {0, 1, 4, 5} mod 7.

0, 1, 4, 5, 7, 8, 11, 12, 14, 15, 18, 19, 21, 22, 25, 26, 28, 29, 32, 33, 35, 36, 39, 40, 42, 43, 46, 47, 49, 50, 53, 54, 56, 57, 60, 61, 63, 64, 67, 68, 70, 71, 74, 75, 77, 78, 81, 82, 84, 85, 88, 89, 91, 92, 95, 96, 98, 99, 102, 103, 105, 106, 109, 110

Offset

1,3

Links

Table of n, a(n) for n=1..64.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(1)=4 and b(k)=7*2^(k-2) for k>1. - Philippe Deléham, Oct 25 2011

G.f.: x^2*(1+3*x+x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011

From Wesley Ivan Hurt, May 24 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (14*n-15-3*i^(2*n)+(1-i)*i^(-n)+(1+i)*i^n)/8, where i=sqrt(-1).

a(2k) = A047383(k), a(2k-1) = A047345(k). (End)

E.g.f.: (8 - sin(x) + cos(x) + (7*x - 6)*sinh(x) + (7*x - 9)*cosh(x))/4. - Ilya Gutkovskiy, May 25 2016

Maple

A047377:=n->(14*n-15-3*I^(2*n)+(1-I)*I^(-n)+(1+I)*I^n)/8: seq(A047377(n), n=1..100); # Wesley Ivan Hurt, May 24 2016

Mathematica

Table[(14n-15-3*I^(2n)+(1-I)*I^(-n)+(1+I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 24 2016 *)
Select[Range@ 120, MemberQ[{0, 1, 4, 5}, Mod[#, 7]] &] (* Michael De Vlieger, May 24 2016 *)
a[n_] :=  n + Floor[(n - 1)/2] +  Floor[(n - 3)/4];
Table[a[n], {n, 1, 64}] (* Peter Luschny, Dec 23 2021 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [0, 1, 4, 5]]; // Wesley Ivan Hurt, May 24 2016

Crossrefs

Cf. A030308, A047345, A047383.

Sequence in context: A288931 A191276 A228919 * A188265 A032714 A032702

Adjacent sequences: A047374 A047375 A047376 * A047378 A047379 A047380

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Wesley Ivan Hurt, May 24 2016

Status

approved